TSTP Solution File: SWV117+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV117+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:02 EDT 2022
% Result : Theorem 0.22s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV117+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 01:49:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.55 % SZS status Theorem
% 0.22/0.55 % SZS output start Proof
% 0.22/0.55 tff(leq_type, type, (
% 0.22/0.55 leq: ( $i * $i ) > $o)).
% 0.22/0.55 tff(minus_type, type, (
% 0.22/0.55 minus: ( $i * $i ) > $i)).
% 0.22/0.55 tff(succ_type, type, (
% 0.22/0.55 succ: $i > $i)).
% 0.22/0.55 tff(tptp_minus_1_type, type, (
% 0.22/0.55 tptp_minus_1: $i)).
% 0.22/0.55 tff(a_select3_type, type, (
% 0.22/0.55 a_select3: ( $i * $i * $i ) > $i)).
% 0.22/0.55 tff(tptp_fun_O_19_type, type, (
% 0.22/0.55 tptp_fun_O_19: $i)).
% 0.22/0.55 tff(id_ds1_filter_type, type, (
% 0.22/0.55 id_ds1_filter: $i)).
% 0.22/0.55 tff(plus_type, type, (
% 0.22/0.55 plus: ( $i * $i ) > $i)).
% 0.22/0.55 tff(n5_type, type, (
% 0.22/0.55 n5: $i)).
% 0.22/0.55 tff(pred_type, type, (
% 0.22/0.55 pred: $i > $i)).
% 0.22/0.55 tff(n1_type, type, (
% 0.22/0.55 n1: $i)).
% 0.22/0.55 tff(tptp_fun_P_20_type, type, (
% 0.22/0.55 tptp_fun_P_20: $i)).
% 0.22/0.55 tff(tptp_fun_J_13_type, type, (
% 0.22/0.55 tptp_fun_J_13: $i)).
% 0.22/0.55 tff(tptp_fun_I_14_type, type, (
% 0.22/0.55 tptp_fun_I_14: $i)).
% 0.22/0.55 tff(q_ds1_filter_type, type, (
% 0.22/0.55 q_ds1_filter: $i)).
% 0.22/0.55 tff(n6_type, type, (
% 0.22/0.55 n6: $i)).
% 0.22/0.55 tff(n0_type, type, (
% 0.22/0.55 n0: $i)).
% 0.22/0.55 tff(pminus_ds1_filter_type, type, (
% 0.22/0.55 pminus_ds1_filter: $i)).
% 0.22/0.55 tff(r_ds1_filter_type, type, (
% 0.22/0.55 r_ds1_filter: $i)).
% 0.22/0.55 tff(n3_type, type, (
% 0.22/0.55 n3: $i)).
% 0.22/0.55 tff(n999_type, type, (
% 0.22/0.55 n999: $i)).
% 0.22/0.55 tff(pv5_type, type, (
% 0.22/0.55 pv5: $i)).
% 0.22/0.55 tff(tptp_fun_N_17_type, type, (
% 0.22/0.55 tptp_fun_N_17: $i)).
% 0.22/0.55 tff(tptp_fun_M_18_type, type, (
% 0.22/0.55 tptp_fun_M_18: $i)).
% 0.22/0.55 tff(tptp_fun_L_15_type, type, (
% 0.22/0.55 tptp_fun_L_15: $i)).
% 0.22/0.55 tff(tptp_fun_K_16_type, type, (
% 0.22/0.55 tptp_fun_K_16: $i)).
% 0.22/0.55 tff(1,plain,
% 0.22/0.55 (^[X: $i] : refl((plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))) <=> (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(2,plain,
% 0.22/0.55 (![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.55 tff(3,plain,
% 0.22/0.55 (^[X: $i] : rewrite((plus(X, n5) = succ(succ(succ(succ(succ(X)))))) <=> (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(4,plain,
% 0.22/0.55 (![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.55 tff(5,plain,
% 0.22/0.55 (![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X))))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(6,axiom,(![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_plus_5_r')).
% 0.22/0.55 tff(7,plain,
% 0.22/0.55 (![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X))))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.55 tff(8,plain,
% 0.22/0.55 (![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.22/0.55 tff(9,plain,(
% 0.22/0.55 ![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.22/0.55 inference(skolemize,[status(sab)],[8])).
% 0.22/0.55 tff(10,plain,
% 0.22/0.55 (![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.55 tff(11,plain,
% 0.22/0.55 ((~![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))) | (plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(12,plain,
% 0.22/0.55 (plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.22/0.55 tff(13,plain,
% 0.22/0.55 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(14,plain,
% 0.22/0.55 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(15,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.22/0.55 tff(16,plain,
% 0.22/0.55 (![X: $i] : (pred(succ(X)) = X)),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.55 tff(17,plain,(
% 0.22/0.55 ![X: $i] : (pred(succ(X)) = X)),
% 0.22/0.55 inference(skolemize,[status(sab)],[16])).
% 0.22/0.55 tff(18,plain,
% 0.22/0.55 (![X: $i] : (pred(succ(X)) = X)),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.22/0.55 tff(19,plain,
% 0.22/0.55 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) = succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(20,plain,
% 0.22/0.55 (pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.55 tff(21,plain,
% 0.22/0.55 (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(22,plain,
% 0.22/0.55 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.55 tff(23,plain,
% 0.22/0.55 (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(24,plain,
% 0.22/0.55 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.55 tff(25,plain,
% 0.22/0.55 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(26,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.22/0.55 tff(27,plain,
% 0.22/0.55 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.55 tff(28,plain,
% 0.22/0.55 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.22/0.55 tff(29,plain,(
% 0.22/0.55 ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.22/0.55 inference(skolemize,[status(sab)],[28])).
% 0.22/0.55 tff(30,plain,
% 0.22/0.55 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.22/0.55 tff(31,plain,
% 0.22/0.55 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))) = pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(32,plain,
% 0.22/0.55 (minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))) = pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.22/0.55 tff(33,plain,
% 0.22/0.55 (minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))) = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[32, 20])).
% 0.22/0.55 tff(34,plain,
% 0.22/0.55 (plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) = plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[33])).
% 0.22/0.55 tff(35,plain,
% 0.22/0.55 (plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) = succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[34, 12])).
% 0.22/0.55 tff(36,plain,
% 0.22/0.55 (minus(plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))) = minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[35])).
% 0.22/0.55 tff(37,plain,
% 0.22/0.55 (leq(O!19, minus(plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) <=> leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[36])).
% 0.22/0.55 tff(38,plain,
% 0.22/0.55 (leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) <=> leq(O!19, minus(plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.22/0.55 inference(symmetry,[status(thm)],[37])).
% 0.22/0.55 tff(39,assumption,(~((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.22/0.55 tff(40,plain,
% 0.22/0.55 (((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(41,plain,
% 0.22/0.55 (leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.22/0.55 tff(42,plain,
% 0.22/0.55 (((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(43,plain,
% 0.22/0.55 (leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.22/0.55 tff(44,plain,
% 0.22/0.55 (((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), J!13)),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(45,plain,
% 0.22/0.55 (leq(succ(tptp_minus_1), J!13)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[44, 39])).
% 0.22/0.55 tff(46,plain,
% 0.22/0.55 (((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), I!14)),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(47,plain,
% 0.22/0.55 (leq(succ(tptp_minus_1), I!14)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[46, 39])).
% 0.22/0.55 tff(48,plain,
% 0.22/0.55 (((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(49,plain,
% 0.22/0.55 (~(a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[48, 39])).
% 0.22/0.55 tff(50,plain,
% 0.22/0.55 (^[A: $i, B: $i] : refl(((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(51,plain,
% 0.22/0.55 (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.55 tff(52,plain,
% 0.22/0.55 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(53,plain,
% 0.22/0.55 (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[52])).
% 0.22/0.55 tff(54,plain,
% 0.22/0.55 (^[A: $i, B: $i] : rewrite(((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(55,plain,
% 0.22/0.55 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[54])).
% 0.22/0.55 tff(56,plain,
% 0.22/0.55 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(57,plain,
% 0.22/0.55 ((~((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i] : ((leq(n0, G) & leq(G, minus(plus(n1, minus(n6, n1)), n1))) => ![H: $i] : ((leq(n0, H) & leq(H, minus(n6, n1))) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, minus(n6, n1))) & leq(J, minus(n6, n1))) => (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I)))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n3, n1))) & leq(L, minus(n3, n1))) => (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n6, n1))) & leq(N, minus(n6, n1))) => (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M)))) & ![O: $i] : ((leq(n0, O) & leq(O, minus(n6, n1))) => ![P: $i] : ((leq(n0, P) & leq(P, minus(n6, n1))) => (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))) <=> (~((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i] : ((~(leq(n0, G) & leq(G, minus(plus(n1, minus(n6, n1)), n1)))) | ![H: $i] : ((~(leq(n0, H) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(58,axiom,(~((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i] : ((leq(n0, G) & leq(G, minus(plus(n1, minus(n6, n1)), n1))) => ![H: $i] : ((leq(n0, H) & leq(H, minus(n6, n1))) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, minus(n6, n1))) & leq(J, minus(n6, n1))) => (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I)))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n3, n1))) & leq(L, minus(n3, n1))) => (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n6, n1))) & leq(N, minus(n6, n1))) => (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M)))) & ![O: $i] : ((leq(n0, O) & leq(O, minus(n6, n1))) => ![P: $i] : ((leq(n0, P) & leq(P, minus(n6, n1))) => (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0010')).
% 0.22/0.56 tff(59,plain,
% 0.22/0.56 (~((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i] : ((~(leq(n0, G) & leq(G, minus(plus(n1, minus(n6, n1)), n1)))) | ![H: $i] : ((~(leq(n0, H) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.56 tff(60,plain,
% 0.22/0.56 (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i] : ((~(leq(n0, G) & leq(G, minus(plus(n1, minus(n6, n1)), n1)))) | ![H: $i] : ((~(leq(n0, H) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))),
% 0.22/0.56 inference(or_elim,[status(thm)],[59])).
% 0.22/0.56 tff(61,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.22/0.56 inference(and_elim,[status(thm)],[60])).
% 0.22/0.56 tff(62,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.22/0.56 tff(63,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.22/0.56 tff(64,plain,(
% 0.22/0.56 ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.22/0.56 inference(skolemize,[status(sab)],[63])).
% 0.22/0.56 tff(65,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[64, 53])).
% 0.22/0.56 tff(66,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[65, 51])).
% 0.22/0.56 tff(67,plain,
% 0.22/0.56 (((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(68,plain,
% 0.22/0.56 ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(69,plain,
% 0.22/0.56 ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.22/0.56 tff(70,plain,
% 0.22/0.56 ($false),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[69, 66, 49, 47, 45, 43, 41])).
% 0.22/0.56 tff(71,plain,((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.56 tff(72,assumption,(~((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.22/0.56 tff(73,plain,
% 0.22/0.56 (((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(74,plain,
% 0.22/0.56 (leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.22/0.56 tff(75,plain,
% 0.22/0.56 (((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(76,plain,
% 0.22/0.56 (leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.22/0.56 tff(77,plain,
% 0.22/0.56 (((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), N!17)),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(78,plain,
% 0.22/0.56 (leq(succ(tptp_minus_1), N!17)),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[77, 72])).
% 0.22/0.56 tff(79,plain,
% 0.22/0.56 (((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), M!18)),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(80,plain,
% 0.22/0.56 (leq(succ(tptp_minus_1), M!18)),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[79, 72])).
% 0.22/0.56 tff(81,plain,
% 0.22/0.56 (((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(82,plain,
% 0.22/0.56 (~(a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[81, 72])).
% 0.22/0.56 tff(83,plain,
% 0.22/0.56 (^[E: $i, F: $i] : refl(((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(84,plain,
% 0.22/0.56 (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[83])).
% 0.22/0.56 tff(85,plain,
% 0.22/0.56 (^[E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> (((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))), rewrite((((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(86,plain,
% 0.22/0.56 (![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[85])).
% 0.22/0.56 tff(87,plain,
% 0.22/0.56 (^[E: $i, F: $i] : rewrite(((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(88,plain,
% 0.22/0.56 (![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[87])).
% 0.22/0.56 tff(89,plain,
% 0.22/0.56 (![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(90,plain,
% 0.22/0.56 (![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.22/0.57 inference(and_elim,[status(thm)],[60])).
% 0.22/0.57 tff(91,plain,
% 0.22/0.57 (![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.57 tff(92,plain,
% 0.22/0.57 (![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.22/0.57 tff(93,plain,(
% 0.22/0.57 ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.22/0.57 inference(skolemize,[status(sab)],[92])).
% 0.22/0.57 tff(94,plain,
% 0.22/0.57 (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.22/0.57 tff(95,plain,
% 0.22/0.57 (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.22/0.57 tff(96,plain,
% 0.22/0.57 (((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(97,plain,
% 0.22/0.57 ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(quant_inst,[status(thm)],[])).
% 0.22/0.57 tff(98,plain,
% 0.22/0.57 ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.22/0.57 tff(99,plain,
% 0.22/0.57 ($false),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[98, 95, 82, 80, 78, 76, 74])).
% 0.22/0.57 tff(100,plain,((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.57 tff(101,assumption,(~((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.22/0.57 tff(102,plain,
% 0.22/0.57 (((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(103,plain,
% 0.22/0.57 (leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.22/0.57 tff(104,plain,
% 0.22/0.57 (((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(105,plain,
% 0.22/0.57 (leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.22/0.57 tff(106,plain,
% 0.22/0.57 (((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), L!15)),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(107,plain,
% 0.22/0.57 (leq(succ(tptp_minus_1), L!15)),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[106, 101])).
% 0.22/0.57 tff(108,plain,
% 0.22/0.57 (((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), K!16)),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(109,plain,
% 0.22/0.57 (leq(succ(tptp_minus_1), K!16)),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[108, 101])).
% 0.22/0.57 tff(110,plain,
% 0.22/0.57 (((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (~(a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(111,plain,
% 0.22/0.57 (~(a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[110, 101])).
% 0.22/0.57 tff(112,plain,
% 0.22/0.57 (^[C: $i, D: $i] : refl(((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(113,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[112])).
% 0.22/0.57 tff(114,plain,
% 0.22/0.57 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> (((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))))), rewrite((((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(115,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[114])).
% 0.22/0.57 tff(116,plain,
% 0.22/0.57 (^[C: $i, D: $i] : rewrite(((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(117,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[116])).
% 0.22/0.57 tff(118,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(119,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.22/0.57 inference(and_elim,[status(thm)],[60])).
% 0.22/0.57 tff(120,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.57 tff(121,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.22/0.57 tff(122,plain,(
% 0.22/0.57 ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.22/0.57 inference(skolemize,[status(sab)],[121])).
% 0.22/0.57 tff(123,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.22/0.57 tff(124,plain,
% 0.22/0.57 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.22/0.57 tff(125,plain,
% 0.22/0.57 (((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) <=> ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(126,plain,
% 0.22/0.57 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.22/0.57 inference(quant_inst,[status(thm)],[])).
% 0.22/0.58 tff(127,plain,
% 0.22/0.58 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.22/0.58 tff(128,plain,
% 0.22/0.58 ($false),
% 0.22/0.58 inference(unit_resolution,[status(thm)],[127, 124, 111, 109, 107, 105, 103])).
% 0.22/0.58 tff(129,plain,((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.58 tff(130,plain,
% 0.22/0.58 (((~((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), O!19)) | (~leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), O!19)) | (~leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(131,plain,
% 0.22/0.58 ((leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> (~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), O!19)) | (~leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(132,plain,
% 0.22/0.58 ((~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))) <=> (~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(133,plain,
% 0.22/0.58 ((leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))) <=> (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.22/0.58 inference(monotonicity,[status(thm)],[132])).
% 0.22/0.58 tff(134,plain,
% 0.22/0.58 ((leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))) <=> (~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), O!19)) | (~leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.58 inference(transitivity,[status(thm)],[133, 131])).
% 0.22/0.58 tff(135,plain,
% 0.22/0.58 ((~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) <=> (~((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(136,plain,
% 0.22/0.58 ((~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) <=> (~((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(137,plain,
% 0.22/0.58 ((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) <=> (~((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(138,plain,
% 0.22/0.58 (((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))) <=> ((~((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), O!19)) | (~leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.22/0.58 inference(monotonicity,[status(thm)],[137, 136, 135, 134])).
% 0.22/0.58 tff(139,plain,
% 0.22/0.58 (((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))) <=> ((~((a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)) | (~leq(succ(tptp_minus_1), P!20)) | (~leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), O!19)) | (~leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)) | (~leq(succ(tptp_minus_1), I!14)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)) | (~leq(succ(tptp_minus_1), K!16)) | (~leq(succ(tptp_minus_1), L!15)) | (~leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)) | (~leq(succ(tptp_minus_1), M!18)) | (~leq(succ(tptp_minus_1), N!17)) | (~leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.22/0.58 inference(transitivity,[status(thm)],[138, 130])).
% 0.22/0.58 tff(140,plain,
% 0.22/0.58 (((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(141,plain,
% 0.22/0.58 (((leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))) <=> (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(142,plain,
% 0.22/0.58 ((~(~(leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(143,plain,
% 0.22/0.58 (((~(~(leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))) <=> ((leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))),
% 0.22/0.58 inference(monotonicity,[status(thm)],[142])).
% 0.22/0.58 tff(144,plain,
% 0.22/0.58 (((~(~(leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))) <=> (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))),
% 0.22/0.59 inference(transitivity,[status(thm)],[143, 141])).
% 0.22/0.59 tff(145,plain,
% 0.22/0.59 (((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | ((~(~(leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))))),
% 0.22/0.59 inference(monotonicity,[status(thm)],[144])).
% 0.22/0.59 tff(146,plain,
% 0.22/0.59 (((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | ((~(~(leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), I!14) & leq(succ(tptp_minus_1), J!13) & leq(I!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I!14, J!13) = a_select3(q_ds1_filter, J!13, I!14)))) | (~((~(leq(succ(tptp_minus_1), K!16) & leq(succ(tptp_minus_1), L!15) & leq(K!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K!16, L!15) = a_select3(r_ds1_filter, L!15, K!16)))) | (~((~(leq(succ(tptp_minus_1), M!18) & leq(succ(tptp_minus_1), N!17) & leq(M!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M!18, N!17) = a_select3(pminus_ds1_filter, N!17, M!18)))) | (leq(succ(tptp_minus_1), O!19) & leq(O!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), P!20) & leq(P!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O!19, P!20) = a_select3(id_ds1_filter, P!20, O!19))))))),
% 0.22/0.59 inference(transitivity,[status(thm)],[145, 140])).
% 0.22/0.59 tff(147,plain,
% 0.22/0.59 ((![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))) <=> (![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(148,plain,
% 0.22/0.59 ((~(![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))) <=> (~(![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))),
% 0.22/0.59 inference(monotonicity,[status(thm)],[147])).
% 0.22/0.59 tff(149,plain,
% 0.22/0.59 ((~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))) <=> (~(![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(150,plain,
% 0.22/0.59 ((![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))) <=> (![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(151,plain,
% 0.22/0.59 ((~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))) <=> (~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[150])).
% 0.54/0.60 tff(152,plain,
% 0.54/0.60 ((~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))) <=> (~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(153,plain,
% 0.54/0.60 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))) <=> (~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(154,plain,
% 0.54/0.60 ((leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))) <=> (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(155,plain,
% 0.54/0.60 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O))))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[154])).
% 0.54/0.60 tff(156,plain,
% 0.54/0.60 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.60 inference(or_elim,[status(thm)],[59])).
% 0.54/0.60 tff(157,plain,
% 0.54/0.60 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.54/0.60 tff(158,plain,
% 0.54/0.60 (~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.54/0.60 tff(159,plain,
% 0.54/0.60 (~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[158, 152])).
% 0.54/0.60 tff(160,plain,
% 0.54/0.60 (~(![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n6, n1)) & leq(J, minus(n6, n1)))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n3, n1)) & leq(L, minus(n3, n1)))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n6, n1)) & leq(N, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(n0, O) & leq(O, minus(n6, n1)))) | ![P: $i] : ((~(leq(n0, P) & leq(P, minus(n6, n1)))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[159, 151])).
% 0.54/0.60 tff(161,plain,
% 0.54/0.60 (~(![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[160, 149])).
% 0.54/0.60 tff(162,plain,
% 0.54/0.60 (~(![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[161, 148])).
% 0.54/0.61 tff(163,plain,
% 0.54/0.61 (~(![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[162, 148])).
% 0.54/0.61 tff(164,plain,
% 0.54/0.61 (~(![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, I, J) = a_select3(q_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, K, L) = a_select3(r_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, M, N) = a_select3(pminus_ds1_filter, N, M))) & ![O: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | ![P: $i] : ((~(leq(succ(tptp_minus_1), P) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, O, P) = a_select3(id_ds1_filter, P, O)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[163, 148])).
% 0.54/0.61 unexpected number of arguments: (let ((a!1 (forall ((I $i) (J $i))
% 0.54/0.61 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.54/0.61 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.54/0.61 (succ (succ tptp_minus_1)))))
% 0.54/0.61 (let ((a!3 (not (and (leq (succ tptp_minus_1) I)
% 0.54/0.61 (leq (succ tptp_minus_1) J)
% 0.54/0.61 (leq I a!2)
% 0.54/0.61 (leq J a!2)))))
% 0.54/0.61 (or a!3
% 0.54/0.61 (= (a_select3 q_ds1_filter I J) (a_select3 q_ds1_filter J I))))))))
% 0.54/0.61 (a!2 (succ (succ (succ (succ tptp_minus_1)))))
% 0.54/0.61 (a!6 (forall ((K $i) (L $i))
% 0.54/0.61 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.54/0.61 (let ((a!2 (leq K (minus a!1 (succ (succ tptp_minus_1)))))
% 0.54/0.61 (a!3 (leq L (minus a!1 (succ (succ tptp_minus_1))))))
% 0.54/0.61 (let ((a!4 (not (and (leq (succ tptp_minus_1) K)
% 0.54/0.61 (leq (succ tptp_minus_1) L)
% 0.54/0.61 a!2
% 0.54/0.61 a!3))))
% 0.54/0.61 (or a!4
% 0.54/0.61 (= (a_select3 r_ds1_filter K L) (a_select3 r_ds1_filter L K))))))))
% 0.54/0.61 (a!11 (forall ((M $i) (N $i))
% 0.54/0.61 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.54/0.61 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.54/0.61 (succ (succ tptp_minus_1)))))
% 0.54/0.61 (let ((a!3 (not (and (leq (succ tptp_minus_1) M)
% 0.54/0.61 (leq (succ tptp_minus_1) N)
% 0.54/0.61 (leq M a!2)
% 0.54/0.61 (leq N a!2)))))
% 0.54/0.61 (or a!3
% 0.54/0.61 (= (a_select3 pminus_ds1_filter M N)
% 0.54/0.61 (a_select3 pminus_ds1_filter N M))))))))
% 0.54/0.61 (a!14 (forall ((O $i))
% 0.54/0.61 (let ((a!1 (succ (succ (succ (succ tptp_minus_1)))))
% 0.54/0.61 (a!4 (forall ((P $i))
% 0.54/0.61 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.54/0.61 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.54/0.61 (succ (succ tptp_minus_1)))))
% 0.54/0.61 (let ((a!3 (not (and (leq (succ tptp_minus_1) P)
% 0.54/0.61 (leq P a!2)))))
% 0.54/0.61 (or a!3
% 0.54/0.61 (= (a_select3 id_ds1_filter O P)
% 0.54/0.61 (a_select3 id_ds1_filter P O)))))))))
% 0.54/0.61 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.54/0.61 (succ (succ tptp_minus_1)))))
% 0.54/0.61 (let ((a!3 (not (and (leq (succ tptp_minus_1) O) (leq O a!2)))))
% 0.54/0.61 (or a!3 a!4))))))
% 0.54/0.61 (a!16 (forall ((P $i))
% 0.54/0.61 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.54/0.61 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.54/0.61 (succ (succ tptp_minus_1)))))
% 0.54/0.61 (let ((a!3 (not (and (leq (succ tptp_minus_1) P) (leq P a!2)))))
% 0.54/0.61 (or a!3
% 0.54/0.61 (= (a_select3 id_ds1_filter O!19 P)
% 0.54/0.61 (a_select3 id_ds1_filter P O!19)))))))))
% 0.54/0.61 (let ((a!3 (minus (succ (succ (succ a!2))) (succ (succ tptp_minus_1))))
% 0.54/0.61 (a!7 (leq K!16 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.54/0.61 (a!8 (leq L!15 (minus a!2 (succ (succ tptp_minus_1))))))
% 0.54/0.61 (let ((a!4 (not (and (leq (succ tptp_minus_1) I!14)
% 0.54/0.61 (leq (succ tptp_minus_1) J!13)
% 0.54/0.61 (leq I!14 a!3)
% 0.54/0.61 (leq J!13 a!3))))
% 0.54/0.61 (a!9 (not (and (leq (succ tptp_minus_1) K!16)
% 0.54/0.61 (leq (succ tptp_minus_1) L!15)
% 0.54/0.61 a!7
% 0.54/0.61 a!8)))
% 0.54/0.61 (a!12 (not (and (leq (succ tptp_minus_1) M!18)
% 0.54/0.61 (leq (succ tptp_minus_1) N!17)
% 0.54/0.61 (leq M!18 a!3)
% 0.54/0.61 (leq N!17 a!3))))
% 0.54/0.61 (a!15 (not (and (leq (succ tptp_minus_1) O!19) (leq O!19 a!3))))
% 0.54/0.61 (a!18 (not (and (leq (succ tptp_minus_1) P!20) (leq P!20 a!3)))))
% 0.54/0.61 (let ((a!5 (not (or a!4
% 0.54/0.61 (= (a_select3 q_ds1_filter I!14 J!13)
% 0.54/0.61 (a_select3 q_ds1_filter J!13 I!14)))))
% 0.54/0.61 (a!10 (not (or a!9
% 0.54/0.61 (= (a_select3 r_ds1_filter K!16 L!15)
% 0.54/0.61 (a_select3 r_ds1_filter L!15 K!16)))))
% 0.54/0.61 (a!13 (not (or a!12
% 0.54/0.61 (= (a_select3 pminus_ds1_filter M!18 N!17)
% 0.54/0.61 (a_select3 pminus_ds1_filter N!17 M!18)))))
% 0.54/0.61 (a!17 (sk (~ (not a!14) (not (or a!15 a!16)))))
% 0.54/0.61 (a!19 (not (or a!18
% 0.54/0.61 (= (a_select3 id_ds1_filter O!19 P!20)
% 0.54/0.61 (a_select3 id_ds1_filter P!20 O!19))))))
% 0.54/0.61 (let ((a!20 (nnf-neg (refl (~ (not a!15) (not a!15)))
% 0.54/0.61 (sk (~ (not a!16) a!19))
% 0.54/0.61 (~ (not (or a!15 a!16)) (and (not a!15) a!19))))
% 0.54/0.61 (a!22 (~ (not (and a!1 a!6 a!11 a!14))
% 0.54/0.61 (or a!5 a!10 a!13 (and (not a!15) a!19)))))
% 0.54/0.61 (let ((a!21 (trans a!17 a!20 (~ (not a!14) (and (not a!15) a!19)))))
% 0.54/0.61 (nnf-neg (sk (~ (not a!1) a!5))
% 0.54/0.61 (sk (~ (not a!6) a!10))
% 0.54/0.61 (sk (~ (not a!11) a!13))
% 0.54/0.61 a!21
% 0.54/0.61 a!22)))))))
% 0.54/0.61 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------